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Carnot problem of maximum work from a finite resource interacting with environment in a finite time

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  • Sieniutycz, Stanislaw

Abstract

We treat an irreversible extension of the Carnot problem of maximum mechanical work delivered from a system of a finite-resource fluid and a bath fluid. For a derived work functional, Pontryagin's maximum principle is applied to determine optimal states and optimal controls. These are respectively represented by the temperature of the resource fluid, T, and the so-called driving temperature T′, an effective temperature which replaces T in the Carnot efficiency formula. Solution of canonical equations is given and free boundary conditions are discussed. Correspondence is proved between the canonical formalism and that governed by the Hamilton–Jacobi equation. A link is shown between the process duration and the optimal dissipation intensity. Hysteretic properties cause difference between the work supplied and delivered, for inverted end states of the process. The results prove that bounds of the classical availability should be replaced by stronger bounds obtained for finite time processes. Related statistical and stochastic approaches are outlined.

Suggested Citation

  • Sieniutycz, Stanislaw, 1999. "Carnot problem of maximum work from a finite resource interacting with environment in a finite time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(1), pages 234-263.
    • Handle: RePEc:eee:phsmap:v:264:y:1999:i:1:p:234-263
    DOI: 10.1016/S0378-4371(98)00444-0
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    Cited by:

    1. Ahmadi, Mohammad H. & Ahmadi, Mohammad Ali & Sadatsakkak, Seyed Abbas, 2015. "Thermodynamic analysis and performance optimization of irreversible Carnot refrigerator by using multi-objective evolutionary algorithms (MOEAs)," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 1055-1070.
    2. Açıkkalp, Emin, 2015. "Exergetic sustainability evaluation of irreversible Carnot refrigerator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 311-320.

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